Quick and dirty summary

How Claude Shannon revolutionized the world with his information theory and how he was motivated by curiosity and fun and never by ego. Also sheds light on how he thinks: much like a sculptor he strips away assumptions from a problem until he is left with the essence which is clearer much simpler to solve (is this decomposition?). Then he adds the assumptions back in and the problem becomes simpler to solve.

Notebook for
A Mind at Play: How Claude Shannon Invented the Information Age
Soni, Jimmy
Citation (APA): Soni, J. (2017). A Mind at Play: How Claude Shannon Invented the Information Age [Kindle Android version]. Retrieved from Amazon.com
Epigraph
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Geniuses are the luckiest of mortals because what they must do is the same as what they most want to do and, even if their genius is unrecognized in their lifetime, the essential earthly reward is always theirs, the certainty that their work is good and will stand the test of time. One suspects that the geniuses will be least in the Kingdom of Heaven— if, indeed, they ever make it; they have had their reward.—W. H. AUDEN
Introduction
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Claude Elwood Shannon published “the Magna Carta of the Information Age”— invented, in a single stroke, the idea of information.
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But before Shannon, there was precious little sense of information as an idea, a measurable quantity, an object fitted out for hard science. Before Shannon, information was a telegram, a photograph, a paragraph, a song. After Shannon, information was entirely abstracted into bits.
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Maybe it is too much to presume that the character of an age bears some stamp of the character of its founders; but it would be pleasant to think that so much of what is essential to ours was conceived in the spirit of play.
Part 1
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He loved science and disliked facts. Or rather, he disliked the kind of facts that he couldn’t bring under a rule and abstract his way out of. Chemistry in particular tested his patience. It “always seems a little dull to me,” he wrote his science teacher years after; “too many isolated facts and too few general principles for my taste.”
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Most of us, Claude included, are less demanding than we might be in our choice of idols: from the universe of possible heroes, we single out the ones who already remind us of ourselves.
Highlight (yellow) - 2. Ann Arbor > Page 16
Shannon’s variety of indecision, which he never entirely outgrew, would prove crucial to his later work. Someone content to build things might have been happy with a single degree in engineering; someone drawn more to theory might have been satisfied with studying math alone. Shannon, mathematically and mechanically inclined, could not make up his mind, but the result left him trained in two fields that would prove essential to his later successes.
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Maybe this is good news for my want to marry the technical and functional worlds
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a sign that his childhood fascination with codebreaking was starting to pay adult dividends.
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I think this applies to us all. Look at the past at what gave you great joy. Chances are either for taste or skill, the neural pathways have been laid. Cash in on the dividends. Don't let them waste away.
Highlight (yellow) - 3. The Room-Sized Brain > Page 29
Given the pipe wrench, produce the words for that wrench and no other; given the words, produce the wrench. That, Bush taught his students, was the beginning of engineering.
Highlight (yellow) - 3. The Room-Sized Brain > Page 29
“A man learns to use the Calculus as he learns to use the chisel or the file,” said one reformer who helped give engineering education its practical bent in the early century.
Highlight (yellow) - 3. The Room-Sized Brain > Page 31
For the physicist or engineer, two systems that obey the same equations have a kind of identity— or at least an analogy. And that, after all, is all our word analog means. A digital watch is nothing like the sun; an analog watch is the memory of a shadow’s circuit around a dial.
Highlight (yellow) - 4. MIT > Page 35
How is logic like a machine? Here is how one logician explained it around the turn of the twentieth century: “As a material machine is an instrument for economising the exertion of force, so a symbolic calculus is an instrument for economising the exertion of intelligence.” Logic, just like a machine, was a tool for democratizing force: built with enough precision and skill, it could multiply the power of the gifted and the average alike.
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In the 1930s, there were only a handful of people in the world who were skilled in both “symbolic calculus,” or rigorous mathematical logic, and the design of electric circuits. This is less remarkable than it sounds: before the two fields melded in Shannon’s brain, it was hardly thought that they had anything in common. It was one thing to compare logic to a machine— it was another entirely to show that machines could do logic.
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In Michigan, Shannon had learned (in a philosophy class, no less) that any statement of logic could be captured in symbols and equations— and that these equations could be solved with a series of simple, math- like rules. You might prove a statement true or false without ever understanding what it meant. You would be less distracted, in fact, if you chose not to understand it: deduction could be automated. The pivotal figure in this translation from the vagaries of words to the sharpness of math was a nineteenth- century genius named George Boole, a self- taught English mathematician whose cobbler father couldn’t afford to keep him in school beyond the age of sixteen. Not long before Thomson conceived of his first analyzer, Boole had proven himself a prodigy with a book that fully earned its presumptuous title: The Laws of Thought. Those laws, Boole showed, are founded on just a few fundamental operations: for instance, AND, OR, NOT, and IF.
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It’s not so much that a thing is “open” or “closed,” the “yes” or “no” that you mentioned. The real point is that two things in series are described by the word “and” in logic, so you would say this “and” this, while two things in parallel are described by the word “or.” . . . There are contacts which close when you operate the relay, and there are other contacts which open, so the word “not” is related to that aspect of relays. . . . The people who had worked with relay circuits were, of course, aware of how to make these things. But they didn’t have the mathematical apparatus of the Boolean algebra.
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as soon as the equations were worked out, they were as good as built. Circuit design was, for the first time, a science. And turning art into science would be the hallmark of Shannon’s career.
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Indifferent to beauty as all but survival’s side effect, wildly profligate, remorseless: nature and techne aren’t so different.
Highlight (yellow) - 5. A Decidedly Unconventional Type of Youngster > Page 45
It’s been said that most of the great writers have bibliographies, not biographies. The kind of life requisite to their work leaves little behind but the words themselves. Even if we had the questionable privilege of watching them scribble for hours every day, we’d find more of who they were simply in the pages of their books.
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he was distinguished less by quantitative horsepower than by his mastery of model making: the reduction of big problems to their essential core.
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More to the point, it was a matter of deep conviction for Bush that specialization was the death of genius. “In these days, when there is a tendency to specialize so closely, it is well for us to be reminded that the possibilities of being at once broad and deep did not pass with Leonardo da Vinci or even Benjamin Franklin,” Bush said in a speech at MIT. “Men of our profession— we teachers— are bound to be impressed with the tendency of youths of strikingly capable minds to become interested in one small corner of science and uninterested in the rest of the world. . . . It is unfortunate when a brilliant and creative mind insists upon living in a modern monastic cell.”
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“Much of the power and elegance of any mathematical theory,” Shannon wrote, “depends on use of a suitably compact and suggestive notation, which nevertheless completely describes the concepts involved.”
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Dear Dr. Bush . . . I’ve been working on three different ideas simultaneously, and strangely enough it seems a more productive method than sticking to one problem. . . .
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Hello interleaving!
Highlight (yellow) - 7. The Labs > Page 61
Real life mathematics . . . requires barbarians: people willing to fight, to conquer, to build, to understand, with no predetermined idea about which tool should be used.—Bernard Beauzamy
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If Google’s “20 percent time”— the practice that frees one- fifth of a Google employee’s schedule to devote to blue- sky projects— seems like a West Coast indulgence, then Bell Labs’ research operation, buoyed by a federally approved monopoly and huge profit margins, would appear gluttonous by comparison. Its employees were given extraordinary freedom. Figure out, a Bell researcher might be told, how “fundamental questions of physics or chemistry might someday affect communications.” Might someday— Bell researchers were encouraged to think decades down the road, to imagine how technology could radically alter the character of everyday life, to wonder how Bell might “connect all of us, and all of our new machines, together.” One Bell employee of a later era summarized it like this: “When I first came there was the philosophy: look, what you’re doing might not be important for ten years or twenty years, but that’s fine, we’ll be there then.”
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The thinkers who thrived at the Labs were those who, confronted with a nearly limitless field of questions, chose the “right” ones: the ones most fertile of breakthroughs in technique or theory, the ones that opened on broad vistas rather than dead ends. This choice of questions has always been a matter of intuition as much as erudition, the irreducible kernel of art in science.
Part 2
Highlight (yellow) - 15. From Intelligence to Information > Page 133
The real measure of information is not in the symbols we send— it’s in the symbols we could have sent, but did not.
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The information value of a symbol depends on the number of alternatives that were killed off in its choosing. Symbols from large vocabularies bear more information than symbols from small ones. Information measures freedom of choice.
Highlight (yellow) - 16. The Bomb > Page 139
• The information source produces a message.• The transmitter encodes the message into a form capable of being sent as a signal.• The channel is the medium through which the signal passes.• The noise source represents the distortions and corruptions that afflict the signal on its way to the receiver.• The receiver decodes the message, reversing the action of the transmitter.• The destination is the recipient of the message.
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Universal model of messaging.
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What does information really measure? It measures the uncertainty we overcome. It measures our chances of learning something we haven’t yet learned. Or, more specifically: when one thing carries information about another— just as a meter reading tells us about a physical quantity, or a book tells us about a life— the amount of information it carries reflects the reduction in uncertainty about the object.
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The messages that resolve the greatest amount of uncertainty— that are picked from the widest range of symbols with the fairest odds— are the richest in information.
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Information is stochastic. It is neither fully unpredictable nor fully determined.
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If there is a pantheon of such absurd and revealing questions, it ought to include a space for Shannon’s: “Why doesn’t anyone say XFOML RXKHRJFFJUJ?” Investigating that question made clear that our “freedom of speech” is mostly an illusion: it comes from an impoverished understanding of freedom. Freer communicators than us— free, of course, in the sense of uncertainty and information— would say XFOML RXKHRJFFJUJ. But in reality, the vast bulk of possible messages have already been eliminated for us before we utter a word or write a line.
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So to advance human thinking one must reinvent language. Just like what Alan Kay said. Perhaps this can be done aided with code.
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in the end, codebreaking remained possible, and remains so, because every message runs up against a basic reality of human communication. It always involves redundancy; to communicate is to make oneself predictable.
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In Shannon’s terms, the feature of messages that makes code- cracking possible is redundancy. A historian of cryptography, David Kahn, explained it like this: “Roughly, redundancy means that more symbols are transmitted in a message than are actually needed to bear the information.” Information resolves our uncertainty; redundancy is every part of a message that tells us nothing new. Whenever we can guess what comes next, we’re in the presence of redundancy. Letters can be redundant: because Q is followed almost automatically by U, the U tells us almost nothing in its own right. We can usually discard it, and many more letters besides. As Shannon put it, “MST PPL HV LTTL DFFCLTY N RDNG THS SNTNC.”
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In his theory of communication, Shannon guessed that the world’s wealth of English text could be cut in half with no loss of information: “When we write English, half of what we write is determined by the structure of the language and half is chosen freely.” Later on, his estimate of redundancy rose as high as 80 percent: only one in five characters actually bear information.
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Shannon proposed an unsettling inversion. Ignore the physical channel and accept its limits: we can overcome noise by manipulating our messages. The answer to noise is not in how loudly we speak, but in how we say what we say.
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One of the worst things that noise can do— in a burst of static, interference from the atmosphere, or physical damage to the channel— is falsify bits. Where the sender says “1,” the receiver hears “0,” or vice versa. So if we used this code, an error to a single bit could be fatal. If just one of the bits representing C flipped, C would vanish in the channel: it would emerge as B or D, with the receiver none the wiser. It would take just two such flips to turn “DAD” to “CAB.” But we can solve the problem— just as human languages have intuitively, automatically solved the same problem— by adding bits. We could use a code like this: A = 00000 B = 00111 C = 11100 D = 11011 Now any letter could sustain damage to any one bit and still resemble itself more than any other letter.
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As information theorist Dave Forney put it, “bits are the universal interface.”
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We sort the mail, build sand castles, solve jigsaw puzzles, separate wheat from chaff, rearrange chess pieces, collect stamps, alphabetize books, create symmetry, compose sonnets and sonatas, and put our rooms in order. . . . We propagate structure (not just we humans but we who are alive). We disturb the tendency toward equilibrium. It would be absurd to attempt a thermodynamic accounting for such processes, but it is not absurd to say that we are reducing entropy, piece by piece. Bit by bit.
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our tendency to reimagine the universe in the image of our tools. We made clocks, and found the world to be clockwork; steam engines, and found the world to be a machine processing heat; information networks— switching circuits and data transmission and half a million miles of submarine cable connecting the continents— and found the world in their image, too.
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Could a machine think?—Could it be in pain?—Well, is the human body to be called such a machine? It surely comes as close as possible to being such a machine. But a machine surely cannot think!—Is that an empirical statement? No. We only say of a human being and what is like one that it thinks. We also say it of dolls and no doubt of spirits too. —Ludwig Wittgenstein I’m a machine and you’re a machine, and we both think, don’t we? —Claude Shannon
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“I think the history of science has shown that valuable consequences often proliferate from simple curiosity,” Shannon once remarked. Curiosity in extremis runs the risk of becoming dilettantism, a tendency to sample everything and finish nothing. But Shannon’s curiosity was different. His kind meant asking a question and then constructing—usually, with his hands—a plausible answer.
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“My fondest dream is to someday build a machine that really thinks, learns, communicates with humans and manipulates its environment in a fairly sophisticated way,” Shannon admitted. But he was not bothered by the usual fears of a world run by machines or a human race taking a backseat to robots. If anything, Shannon believed the opposite: “In the long run [the machines] will be a boon to humanity, and the point is to make them so as rapidly as possible. . . . There is much greater empathy between man and machines [today] . . . we’d like to close it up so that we are actually talking back and forth.”
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“First, how can we give computers a better sensory knowledge of the real world? Second, how can they better tell us what they know, besides printing out the information? And third, how can we get them to react upon the real world?”
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I believe that today, that we are going to invent something, it’s not going to be the biological process of evolution anymore, it’s going to be the inventive process whereby we invent machines which are smarter than we are and so we’re no longer useful, not only smarter but they last longer and have replaceable parts and they’re so much better. There are so many of these things about the human system, it’s just terrible. The only thing surgeons can do to help you basically is to cut something out of you. They don’t cut it out and put something better in, or a new part in.
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“We artificial intelligence people are insatiable,” he once wrote. Once machines were beating our grandmasters, writing our poetry, completing our mathematical proofs, and managing our money, we would, Shannon observed only half-jokingly, be primed for extinction. “These goals could mark the beginning of a phase-out of the stupid, entropy-increasing, and militant human race in favor of a more logical, energy conserving, and friendly species—the computer.”
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The thought that a machine could never exceed its creator was “just foolish logic, wrong and incorrect logic.” He went on: “you can make a thing that is smarter than yourself. Smartness in this game is made partly of time and speed. I can build something which can operate much faster than my neurons.”
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I think man is a machine. No, I am not joking, I think man is a machine of a very complex sort, different from a computer, i.e., different in organization. But it could be easily reproduced—it has about ten billion nerve cells, i.e., 1010 neurons. And if you model each one of these with electronic equipment it will act like a human brain. If you take [Bobby] Fischer’s head and make a model of that, it would play like Fischer.
Highlight (yellow) - 25. Constructive Dissatisfaction > Page 218
a third quality was still missing—something without which the world would have its full share of competent engineers but would lack even one real innovator. It was here, naturally, that Shannon was at his fuzziest. It is a quality of “motivation . . . some kind of desire to find out the answer, the desire to find out what makes things tick.” For Shannon, this was a requirement: “If you don’t have that, you may have all the training and intelligence in the world, [but] you don’t have the questions and you won’t just find the answers.” Yet he himself was unable to nail down its source. As he put it, “It is a matter of temperament probably; that is, a matter of probably early training, early childhood experiences.” Finally, at a loss for exactly what to call it, he settled on curiosity. “I just won’t go any deeper into it than that.” But then the great insights don’t spring from curiosity alone, but from dissatisfaction—not the depressive kind of dissatisfaction (of which, he did not say, he had experienced his fair share), but rather a “constructive dissatisfaction,” or “a slight irritation when things don’t look quite right.” It was, at least, a refreshingly unsentimental picture of genius: a genius is simply someone who is usefully irritated. And finally: the genius must delight in finding solutions. It must have seemed to Shannon that though many around him were of equal intellect, not everyone derived equal joy from the application of intellect. For his part, “I get a big bang out of proving a theorem. If I’ve been trying to prove a mathematical theorem for a week or so and I finally get the solution, I get a big bang out of it. And I get a big kick out of seeing a clever way of doing some engineering problem, a clever design for a circuit which uses a very small amount of equipment and gets apparently a great deal of result out of it.” For Shannon, there was no substitute for the “pleasure in seeing net results.”
Highlight (yellow) - 25. Constructive Dissatisfaction > Page 219
You might, he said, start by simplifying: “Almost every problem that you come across is befuddled with all kinds of extraneous data of one sort or another; and if you can bring this problem down into the main issues, you can see more clearly what you’re trying to do.”
Highlight (yellow) - 25. Constructive Dissatisfaction > Page 219
Failing this difficult work of simplifying, or supplementing it, you might attempt step two: encircle your problem with existing answers to similar questions, and then deduce what it is that the answers have in common—in fact, if you’re a true expert, “your mental matrix will be filled with P’s and S’s,” a vocabulary of questions already answered. Call it ingenious incrementalism—or, as Shannon put it, “It seems to be much easier to make two small jumps than the one big jump in any kind of mental thinking.”
Highlight (yellow) - 25. Constructive Dissatisfaction > Page 219
If you cannot simplify or solve via similarities, try to restate the question: “Change the words. Change the viewpoint. . . . Break loose from certain mental blocks which are holding you in certain ways of looking at a problem.” Avoid “ruts of mental thinking.” In other words, don’t become trapped by the sunk cost, the work you’ve already put in. There’s a reason, after all, why “someone who is quite green to a problem” will sometimes solve it on their first attempt: they are unconstrained by the biases that build up over time.
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Beginner's Mind and the importance of interleaving and taking breaks.
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one of the most powerful ways of changing the viewpoint is through the “structural analysis of a problem”—that is, through breaking an overwhelming problem into small pieces.
Part 3
Highlight (yellow) - 26. Professor Shannon > Page 232
Robert Gallager, captures both the power and subtlety of Shannon’s approach to the work of instruction: I had what I thought was a really neat research idea, for a much better communication system than what other people were building, with all sorts of bells and whistles. I went in to talk to him about it and I explained the problems I was having trying to analyze it. And he looked at it, sort of puzzled, and said, “Well, do you really need this assumption?” And I said, well, I suppose we could look at the problem without that assumption. And we went on for a while. And then he said, again, “Do you need this other assumption?” And I saw immediately that that would simplify the problem, although it started looking a little impractical and a little like a toy problem. And he kept doing this, about five or six times. I don’t think he saw immediately that that’s how the problem should be solved; I think he was just groping his way along, except that he just had this instinct of which parts of the problem were fundamental and which were just details. At a certain point, I was getting upset, because I saw this neat research problem of mine had become almost trivial. But at a certain point, with all these pieces stripped out, we both saw how to solve it. And then we gradually put all these little assumptions back in and then, suddenly, we saw the solution to the whole problem. And that was just the way he worked. He would find the simplest example of something and then he would somehow sort out why that worked and why that was the right way of looking at it.
Highlight (yellow) - 27. Inside Information > Page 241
The Shannons had toyed with technical analysis, and they found it wanting. As Shannon himself put it, “I think that the technicians who work so much with price charts, with ‘head and shoulders formulations’ and ‘plunging necklines’ are working with what I would call a very noisy reproduction of the important data.” Complicated formulas mattered a great deal less, Shannon argued, than a company’s “people and the product.” He went on: A lot of people look at the stock price, when they should be looking at the basic company and its earnings. There are many problems concerned with the prediction of stochastic processes, for example the earnings of companies. . . . My general feeling is that it is easier to choose companies which are going to succeed, than to predict short term variations, things which last only weeks or months, which they worry about on Wall Street Week. There is a lot more randomness there and things happen which you cannot predict, which cause people to sell or buy a lot of stock.
Highlight (yellow) - 28. A Gadgeteer’s Paradise > Page 245
“Shannon seemed to think with ‘ideas’ more than with words or formulas. A new problem was like a sculptor’s block of stone and Shannon’s ideas chiseled away the obstacles until an approximate solution emerged like an image, which he proceeded to refine as desired with more ideas.”
Highlight (yellow) - 30. Kyoto > Page 257
I don’t think I was ever motivated by the notion of winning prizes, although I have a couple of dozen of them in the other room. I was more motivated by curiosity. Never by the desire for financial gain. I just wondered how things were put together. Or what laws or rules govern a situation, or if there are theorems about what one can’t or can do. Mainly because I wanted to know myself.
Highlight (yellow) - 31. The Illness > Page 272
An unsuspecting visitor would see SHANNON engraved in pale gray marble and move on. What’s concealed, however, is a message on the reverse: covered by a bush, the open section of the marble on the back of the tombstone holds Shannon’s entropy formula. Shannon’s children had hoped the formula would grace the front of the stone; their mother thought it more modest to engrave it on the back. And so Claude Shannon’s resting place is marked by a kind of code: a message hidden from view, invisible except to those looking for it.
Highlight (yellow) - 32. Aftershocks > Page 275
Shannon’s body of work is a useful corrective to our era of unprecedented specialization. His work is wide-ranging in the best sense, and perhaps more than any twentieth-century intellect of comparable stature, he resists easy categorization. Was he a mathematician? Yes. Was he an engineer? Yes. Was he a juggler, unicyclist, machinist, futurist, and gambler? Yes, and then some. Shannon never acknowledged the contradictions in his fields of interest; he simply went wherever his omnivorous curiosity led him. So it was entirely consistent for him to jump from information theory to artificial intelligence to chess to juggling to gambling—it simply didn’t occur to him that investing his talents in a single field made any sense at all.
Highlight (yellow) - 32. Aftershocks > Page 277
Courage is one of the things that Shannon had supremely. You have only to think of his major theorem. He wants to create a method of coding, but he doesn’t know what to do so he makes a random code. Then he is stuck. And then he asks the impossible question, “What would the average random code do?” He then proves that the average code is arbitrarily good, and that therefore there must be at least one good code. Who but a man of infinite courage could have dared to think those thoughts? That is the characteristic of great scientists; they have courage. They go forward under incredible circumstances; they think and continue to think.
Highlight (yellow) - 32. Aftershocks > Page 278
the other great hallmark of Shannon’s life: the value of finding joy in work. We expect our greatest minds to bear the deepest scars; we prefer our geniuses tortured. But with the exception of a few years in his twenties when Shannon passed through what seems like a moody, possibly even depressive, stage, his life and work seemed to be one continuous game. He was, at once, abnormally brilliant and normally human.
Acknowledgments
Highlight (yellow) - 32. Aftershocks > Page 283
Modern man lives isolated in his artificial environment, not because the artificial is evil as such, but because of his lack of comprehension of the forces which make it work—of the principles which relate his gadgets to the forces of nature, to the universal order. It is not central heating which makes his existence “unnatural,” but his refusal to take an interest in the principles behind it. By being entirely dependent on science, yet closing his mind to it, he leads the life of an urban barbarian.